Pre-Calc Homework Solutions 386

# Pre-Calc Homework Solutions 386 - 386 Section 9.5 1 1 1 1 1...

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51. s 1 5 tan 2 1 1 2 tan 2 1 2 5 } p 4 } 2 tan 2 1 2 s 2 5 (tan 2 1 1 2 tan 2 1 2) 1 (tan 2 1 2 2 tan 2 1 3) 5 } p 4 } 2 tan 2 1 3 s 3 5 (tan 2 1 1 2 tan 2 1 2) 1 (tan 2 1 2 2 tan 2 1 3) 1 (tan 2 1 3 2 tan 2 1 4) 5 } p 4 } 2 tan 2 1 4 s n 5 } p 4 } 2 tan 2 1 ( n 1 1) S 5 lim n s n 5 } p 4 } 2 lim n tan 2 1 n 5 } p 4 } 2 } p 2 } 5 2 } p 4 } 52. } 1 2 1 x } 5 n 5 0 x n Differentiate: } (1 2 1 x ) 2 } 5 n 5 0 nx n 2 1 Multiply by x: } (1 2 x x ) 2 } 5 n 5 0 nx n Differentiate: } d d x } } (1 2 x x ) 2 } 5 5 } (1 ( 2 1 2 x ) x 1 ) 3 2 x } 5 } (1 x 2 1 x 1 ) 3 } } (1 x 2 1 x 1 ) 3 } 5 n 5 0 n 2 x n 2 1 Multiply by x: } x (1 ( x 2 1 x 1 ) 3 ) } 5 n 5 0 n 2 x n Let x 5 } 1 2 } : 5 n 5 0 n 2 1 } 1 2 } 2 n 6 5 n 5 0 } 2 n 2 n } The sum is 6. Section 9.5 Testing Convergence at Endpoints (pp. 496–508) Exploration 1 The p -Series Test 1. We first note that the Integral Test applies to any series of the form } n 1 p } where p is positive. This is because the function f ( x ) 5 x 2 p is continuous and positive for all x . 0, and f 9 ( x ) 5 2 p ?
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